I think you might be thinking of "Strike It Rich" (1990) starring the similar-looking Robert Lindsay & Molly Ringwald as the American girl. See link Strike It Rich (1990) - IMDb.
A question on another thread brought to mind the actor Michael Maloney and I started thinking of another film I saw years ago (10 or 15 years ago) which Im pretty sure he was in, though I could have got him misplaced! Any way it concerns a British guy who goes to Monte Carlo and hooks up with a very lovely American girl, he has a theory or philosophy which is I think more a faith than anything, but he claims to have found a way to beat the odds on the gambling tables, Romance ensues and there is an element of danger in the whole adventure, it might have been a period piece can't quite remember, but Im sure it was a TV film. I've looked at Michael Maloney's filmography and cant see what it might be so it may not have been him that was in it..sorry to be so vague..
I think you might be thinking of "Strike It Rich" (1990) starring the similar-looking Robert Lindsay & Molly Ringwald as the American girl. See link Strike It Rich (1990) - IMDb.
Yep, thanks for that, that was the film I was thinking of, so Robert Lindsay rather than Michael Maloney.